Athermal Energy Loss from X-rays Deposited in Thin Superconducting Films on Solid Substrates

When energy is deposited in a thin-film cryogenic detector, such as from the absorption of an X-ray, an important feature that determines the energy resolution is the amount of athermal energy that can be lost to the heat bath prior to the elementary excitation systems coming into thermal equilibrium. This form of energy loss will be position-dependent and therefore can limit the detector energy resolution. An understanding of the physical processes that occur when elementary excitations are generated in metal films on dielectric substrates is important for the design and optimization of a number of different types of low temperature detector. We have measured the total energy loss in one relatively simple geometry that allows us to study these processes and compare measurements with calculation based upon a model for the various di.erent processes. We have modeled the athermal phonon energy loss in this device by finding an evolving phonon distribution function that solves the system of kinetic equations for the interacting system of electrons and phonons. Using measurements of device parameters such as the Debye energy and the thermal di.usivity we have calculated the expected energy loss from this detector geometry, and also the position-dependent variation of this loss. We have also calculated the predicted impact on measured spectral line-shapes, and shown that they agree well with measurements. In addition, we have tested this model by using it to predict the performance of a number of other types of detector with di.erent geometries, where good agreement is also found.